Short Range Ordering in Entropy Stabilized Oxides with the α-PbO₂ Structure

The four-component medium entropy oxide (Ti, Zr, Hf, Sn)O₂crystallizes in the α-PbO₂ structure. The formation of this structure type is interesting since it is distinct from the ground state structure of any of its precursor oxides. In itself, this is an indication that (Ti, Zr, Hf, Sn)O₂might be an entropy stabilized compound. Conveniently, the two-component low entropy oxide (Ti, Zr)O₂crystallizes in the same crystal structure, and is verified experimentally to be entropy stabilized.<br/><br/>Short range ordering (SRO) is an elusive phenomenon to characterize and quantize, but also potentially pivotal for the emergence of superior functional properties in high entropy materials. (Ti, Zr)O₂possesses a well-characterized type of ordering where Ti and Zr cations order in alternating slabs. The degree of ordering can be controlled by the cooling rate and monitored through a simple measurement of the lattice parameters. In this work, we aim to quantify and compare the degree of SRO in the two-component (Ti, Zr)O₂ and the four-component (Ti, Zr, Hf, Sn)O₂.<br/><br/>Pair distribution function measurements reveal large changes in the local structure of (Ti, Zr)O₂ depending on whether the sample has been quenched or slowly cooled, while (Ti, Zr, Hf, Sn)O₂ displays no discernible changes after heat treatments. In order to explain these observations and quantify the true configurational entropy of these materials, we use a computational approach based on density functional theory, cluster expansions, and Metropolis Monte Carlo simulated annealing. The calculations are able to reproduce the type of ordering and temperature range experimentally observed for (Ti, Zr)O₂. The same calculations are performed for (Ti, Zr, Hf, Sn)O₂, where the order-disorder phase transition temperature is lowered by hundreds of degrees relative to the two-component compound. Sluggish diffusion kinetics keep the cations frozen in place regardless of cooling rate, effectively hindering any degree of SRO or even a reversible phase transition, explaining the lack of changes in the pair distribution functions. The two-component compound on the other hand, shows signs of SRO even at synthesis temperature, indicating that the ideal configurational entropy state is never reached. As the energetics of cation-cation interactions are similar in these two materials, it is the increase in configurational entropy that causes the suppression of SRO. Finally, we introduce the possibility of heterovalent substitutions within this framework. In this case, short range order is expected to be strong due to the strong and long-ranged electrostatic forces involved.